Related papers: Generalized Naming Game and Bayesian Naming Game a…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
We develop a hierarchical Bayesian dynamic game for competitive inventory and pricing under incomplete information. Two firms repeatedly choose order quantities and prices while facing two layers of uncertainty: unknown market demand and…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
We study adaptive learning in a typical p-player game. The payoffs of the games are randomly generated and then held fixed. The strategies of the players evolve through time as the players learn. The trajectories in the strategy space…
Deep learning models, including modern systems like large language models, are well known to offer unreliable estimates of the uncertainty of their decisions. In order to improve the quality of the confidence levels, also known as…
Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint…
Generalization analyses of deep learning typically assume that the training converges to a fixed point. But, recent results indicate that in practice, the weights of deep neural networks optimized with stochastic gradient descent often…
This paper studies a dynamic discrete-time queuing model where at every period players get a new job and must send all their jobs to a queue that has a limited capacity. Players have an incentive to send their jobs as late as possible;…
While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the…
In the context of discrete dynamical systems and their applications, fixed points often have a clear interpretation. This is indeed a central topic of gene regulatory mechanisms modeled by Boolean automata networks (BANs), where a…
Event data consisting of time of occurrence of the events arises in several real-world applications. Recent works have introduced neural network based point processes for modeling event-times, and were shown to provide state-of-the-art…
A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often…
In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of…
The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the…
Among the main features of biological intelligence are energy efficiency, capacity for continual adaptation, and risk management via uncertainty quantification. Neuromorphic engineering has been thus far mostly driven by the goal of…
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…
We introduce a game-theoretic framework to study the hypothesis testing problem, in the presence of an adversary aiming at preventing a correct decision. Specifically, the paper considers a scenario in which an analyst has to decide whether…
Recurrent neural networks (RNNs) are popular machine learning tools for modeling and forecasting sequential data and for inferring dynamical systems (DS) from observed time series. Concepts from DS theory (DST) have variously been used to…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
Machine learning models are vulnerable to adversarial examples: minor perturbations to input samples intended to deliberately cause misclassification. While an obvious security threat, adversarial examples yield as well insights about the…